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We show that $K|k$ can be functorially reconstructed by group theoretical recipes from $\\Pi^c_K$ endowed with the set of divisorial inertia ${\\rm Inrdiv}(K)\\subset\\Pi_K$. As applications, one has: (i) A group theoretical recipe to reconstruct $K|k$ from $\\Pi^c_K$, provided either ${\\rm Tr.deg}(K|k)>{\\rm dim}(k)+1$ or ${\\rm tr.deg}(K|k) >{\\rm dim}(k)>1$, where ${\\rm dim}(k)$ is the Kronecker dimension; (ii) An a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.04768","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-10-10T22:40:02Z","cross_cats_sorted":[],"title_canon_sha256":"f48000a40845568ef774e95d54ed1385dc0242a0933fa484e42d2d187c42f16f","abstract_canon_sha256":"18e73c4843a3c6515b692a0d76fe441091c0bb7bc0e23804f3b69cd99e735a60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:35.943195Z","signature_b64":"LiDntnqUMrZQKDUFQHqwJesO8JvEKvcy7Ya2WPONPaM5HNDChVrNgvhhxUpFLGoeHnQld2hn7bJKNab0fT1aBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df46f0ef15a339b7aa011e8931a67474a62082bd7780fa631b7e80e0c5e71737","last_reissued_at":"2026-05-18T00:03:35.942431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:35.942431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconstruction of Function Fields from their pro-l abelian divisorial Inertia","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Florian Pop","submitted_at":"2018-10-10T22:40:02Z","abstract_excerpt":"Let $\\Pi^c_K\\to\\Pi_K$ be the maximal pro-$\\ell$ abelian-by-central, respectively abelian, Galois groups of a function field $K|k$ with $k$ algebraically closed and ${\\rm char}\\neq\\ell$. We show that $K|k$ can be functorially reconstructed by group theoretical recipes from $\\Pi^c_K$ endowed with the set of divisorial inertia ${\\rm Inrdiv}(K)\\subset\\Pi_K$. As applications, one has: (i) A group theoretical recipe to reconstruct $K|k$ from $\\Pi^c_K$, provided either ${\\rm Tr.deg}(K|k)>{\\rm dim}(k)+1$ or ${\\rm tr.deg}(K|k) >{\\rm dim}(k)>1$, where ${\\rm dim}(k)$ is the Kronecker dimension; (ii) An a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04768","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.04768","created_at":"2026-05-18T00:03:35.942530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.04768v1","created_at":"2026-05-18T00:03:35.942530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04768","created_at":"2026-05-18T00:03:35.942530+00:00"},{"alias_kind":"pith_short_12","alias_value":"35DPB3YVUM43","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"35DPB3YVUM43PKQB","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"35DPB3YV","created_at":"2026-05-18T12:32:02.567920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS","json":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS.json","graph_json":"https://pith.science/api/pith-number/35DPB3YVUM43PKQBD2ETDJTUOS/graph.json","events_json":"https://pith.science/api/pith-number/35DPB3YVUM43PKQBD2ETDJTUOS/events.json","paper":"https://pith.science/paper/35DPB3YV"},"agent_actions":{"view_html":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS","download_json":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS.json","view_paper":"https://pith.science/paper/35DPB3YV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.04768&json=true","fetch_graph":"https://pith.science/api/pith-number/35DPB3YVUM43PKQBD2ETDJTUOS/graph.json","fetch_events":"https://pith.science/api/pith-number/35DPB3YVUM43PKQBD2ETDJTUOS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS/action/storage_attestation","attest_author":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS/action/author_attestation","sign_citation":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS/action/citation_signature","submit_replication":"https://pith.science/pith/35DPB3YVUM43PKQBD2ETDJTUOS/action/replication_record"}},"created_at":"2026-05-18T00:03:35.942530+00:00","updated_at":"2026-05-18T00:03:35.942530+00:00"}